On Rastall gravity formulation as a $$f(R,\mathcal {L}_m)$$ and a f(R, T) theory

Abstract Rastall introduced a stress-energy tensor whose divergence is proportional to the gradient of Ricci scalar. This proposal leads change in form field equations General Relativity, but it preserves number degrees freedom. Rastall’s can be either interpreted as GR with redefined SET, or imply different physical consequences inside matter sector. We investigate limits under which directly derived from an action, particular two f ( R )-gravity extensions: $$f(R,\mathcal L_m)$$ f ( R , L m ) and , T ). show that there are similarities between these theories, SET cannot fully recovered them, apart certain cases here discussed. It remarkable simple, covariant invertible redefinition one proposed by Rastall, hard implemented action.